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Poisson sigma model on the sphere. (English) Zbl 1247.53092

This paper is devoted to the Poisson sigma model (PSM) on the sphere. Recently, PSM has been extensively studied in the literature due to its role in the theory of deformation quantization. After a review of the relevant notions, the authors recall the Batalin-Vilkovisky formalism, which is useful to quantize the PSM. A construction of the finite dimensional Batalin-Vilkovisky theory is also presented in details. The path integral of the Poisson sigma model on the sphere is then evaluated. The correlators of quantum observables are discussed. In particular, it is proved that for the holomorphic Poisson structure the semiclassical result for the correlators is the full quantum result.

MSC:

53D17 Poisson manifolds; Poisson groupoids and algebroids
58D30 Applications of manifolds of mappings to the sciences
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
81T70 Quantization in field theory; cohomological methods
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